Fluid dynamics originally was based purely on observation of flow phenomena. Early pioneers in the field observed water flowing and smoke rising. Mathematicians developed formulas that attempted to predict flow behavior around simple geometries such as a cylinder. In the early days of flight wind tunnels were constructed to test airfoil shapes for lift, drag, pitching moment, stall characteristics, and additional flight parameters. Others studied flow losses in pipes and ducts using testing and, for very low flows, mathematical models. In the 1970's and 1980's computers became powerful enough and available to a wide group of researchers, and the science of computational fluid dynamics began to grow into a field of study. Today these conventional models can “test” a foil design using a computer, and the results are verified in a wind tunnel. These Computational Fluid Dynamics (CFD) models are typically made in a four-dimensional mathematical space: time and the three principal directions. Within this space, tensor math is used to identify all of the stresses on a flow element in the space at each point in time. Matrices that contain state variables: pressure, density, velocity, temperature, and elemental forces are calculated by solving partial differential equations which conserve mass, momentum, and energy in the model space. Experience and skill of the model operator is required to divide the model space up into flow elements (this is called meshing) that produce results which match test data of actual flow. In regions of the model with large velocity gradients, turbulence will occur. Wikipedia defines turbulence or turbulent flow in fluid dynamics as a flow regime characterized by chaotic property changes, including low momentum diffusion, high momentum convection, and rapid variation of pressure and flow velocity in space and time.
In a turbulent portion of the model the state variables will be in a state of complete confusion and disorder. Many schemes and methods have been developed to attempt to model flow behavior in these regions, most of which focus on the Reynolds decomposition, a mathematical technique to separate the average and fluctuating parts of a quantity. When applied to the governing flow equations, this is called Reynolds-averaged Navier-Stokes equations (RANS). Various models of turbulence are then used with RANS to model turbulence. Popular turbulence models include One-Equation Models such as Spalart-Allmaras and Nut-92; Two-Equation Models such as Menter k-omega SST, Menter k-omega BSL, Wilcox k-omega, Chien k-epsilon, K-kL, and Explicit Algebraic Stress k-omega; Three-Equation Models include K-e-Rt; Three-Equation Models plus Elliptic Relaxation include K-e-zeta-f; Seven-Equation Omega-Based Full Reynolds Stress Models include Wilcox Stress-omega and SSG/LRR; and Seven-Equation Epsilon-Based Full Reynolds Stress Models include GLVY Stress-epsilon.
These efforts have not been fully satisfactory. Further, to implement the models a modeler must have considerable experience and skill to choose the proper turbulence model for a particular problem, its best meshing requirements, how to run the model to best exploit the model, and must know the approximate answer before starting. Thus, a more convenient and efficient method for constructing surfaces for optimizing the fluid flow relative to those surfaces would be beneficial.